Answers to Problems of the week- July 13 to July 17

Rewards for Problems of the week:

5 points for the correct answer at your level; 10 points for the next level; 20 points each for 2+ levels up. 

Lower Elementary:
Question: Freddy’s grandfather reads him a story that is 49 pages long. If it takes Freddy’s Grandfather 2 minutes to read each page, then how long will it take to read the story?
Answer: 1 hour 38 minutes
Solution: Since each page takes 2 minutes to read, we can find the total amount of time the story by taking the number of pages and doubling it: 49 + 49 = 98. So, the story will take 98 minutes to read. Since an hour is 60 minutes, the story will take 1 hour and 98 – 60 = 38 minutes.

Upper Elementary:
Question: Westley is 6 feet tall. He can reach objects 20 inches over his head­—24 inches if he stands on his tiptoes. Can Westley reach a pitcher that is hanging 90 inches off the ground?
Answer: Yes
Solution: Since there are 12 inches in a foot, Westley is 6 × 12 = 72 inches tall. He can reach objects 24 inches over his head, so he can reach up to 72 + 24 = 96 inches off the ground. The pitcher is only 90 inches off the ground, so Westley can easily reach it.

Middle School:
Question: The average rat weighs half a pound. A rodent of unusual size weighs 37.5 pounds. What percentage of a rodent of unusual size’s weight does the average rat weigh?
Answer: 1.3%
Solution: To find out what fractional part of 37.5 pounds a 0.5–pound rat is, we divide 0.5 by 37.5 to get 0.11.3. A rat is therefore 1.3% the size of a rodent of unusual size.

Algebra and Up:
Question: Max and Valerie are mixing a magic potion. Max pours 24 ounces of swamp water into the cauldron. Valerie pours 8 ounces of unicorn snot into the cauldron. How many more ounces of swamp water does Max need to add to the cauldron to dilute the mixture to 20% unicorn snot?
Answer: 8 ounces
Solution: Max and Valerie’s potion is 24 + 8 = 32 ounces in total, and 8 ÷ 32 = 25% of the mixture is unicorn snot. In order for the 8 ounces of unicorn snot to be 20% of the x-ounce mixture, 8 ÷ x = 20% and x = 40 ounces. So, since 40 – 32 = 8, 8 ounces of swamp water must be added to dilute the mixture to 20% unicorn snot.

Challenge problem to take home. 20 points for the correct answer. 

Two thirds of the students in Parkview Elementary School wear something red during the last School Sprit Day. Of the students wearing something red, half of them were wearing red hats. Of the students wearing red hats, two thirds of them are boys. If 53 girls were wearing red hats, how many students are in Parkview Elementary School?

Answer: The key to solve this problem is to figure out what fractional part of the students were wearing red hats. That was one half of two thirds, which is the same as just one third. So one third of the students were wearing red hats. So 53 times 3, 159 is the answer.